Heat transfer by natural convection in a vertical porous layer

Abstract

Heat transfer by a natural convection in a vertical porous layer heated from below and cooled from above is studied analytically. In the case of linear theory, the normal mode technique is used to find the criteria for the onset of convection and it is shown that convection sets in when the cirtical Reyleigh number exceeds π². The nonlinear theory is investigated using normal mode technique combined with the orthonormal sequences which determines the amplitudes and hence the heat transfer. It is shown that uni-cellular pattern exist and the corresponding heat transfer increases with Rayleigh number.